The Manufacture of Curved Crease Surfaces Starting from Kinematic Analysis of Planar Mechanisms
Abstract
:1. Introduction
2. The Analysis of a Planar Mechanism That Generates Connecting Rod Curves
3. Virtual Analysis of the Technological Process to Obtain Free Forms
4. Results and Discussions
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
- Capone, M.; Lanzara, E. Kerf bending: Ruled double curved surfaces manufacturing. In Proceedings of the 22th Conference of the Iberoamerican Society of Digital Graphics, São Carlos, Brazil, 7–9 November 2018. [Google Scholar]
- Rabinovich, M.; Hoffmann, T.; Sorkine-Hornung, O. Modeling curved folding with freeform deformations. ACM Trans. Graph. 2019, 38, 1–12. [Google Scholar] [CrossRef] [Green Version]
- Demaine, E.; Demaine, M.; Koschitz, D.; Tachi, T. Curved Crease Folding a Review on Art, Design and Mathematics. In Proceedings of the 35th Annual Symposium of IABSE/52nd Annual Symposium of IASS/6th International Conference on Space Structures: Taller, Longer, Lighter—Meeting Growing Demand with Limited Resources, London, UK, 20–23 September 2011. [Google Scholar]
- Raducanu, D.; Cojocaru, V.; Raducanu, V.; Nocivin, A.; Serban, N.; Cinca, I.; Cojocaru, E.; Moldovan, L.; Trisca-Rusu, C.; Balkan, I. Design and Optimization of a Curved-Crease-Folding Process Applied to a Light Metallic Structure. Processes 2021, 9, 1110. [Google Scholar] [CrossRef]
- Bacinoglu, S.Z.; Piskorec, L.; Kotnik, T. CURVED.IT: A design tool to integrate making with curved folding into digital design process. A/Z ITU J. Fac. Arch. 2019, 16, 11–27. [Google Scholar] [CrossRef]
- Foschi, R. Algorithmic Modelling of Folded Surfaces. Analysis and Design of Folded Surfaces in Architecture and Manufacturing. Ph.D. Thesis, Alma Mater Studiorum Università di Bologna, Bologna, Italy, 2019. [Google Scholar]
- Chen, Y.; Yan, J.; Feng, J. Geometric and Kinematic Analyses and Novel Characteristics of Origami-Inspired Structures. Symmetry 2019, 11, 1101. [Google Scholar] [CrossRef] [Green Version]
- Available online: https://asm.matweb.com/search/SpecificMaterial.asp?bassnum=ma6061t6 (accessed on 10 June 2022).
- Stachel, H. Remarks on Miura-ori, a Japanese folding method, Acta Technica Napocensis. In Proceedings of the International Conference on Engineering Graphics and Design, Cluj Napoca, Romania, 12–13 June 2009. [Google Scholar]
- Chen, Y.; Guest, S.D.; Fowler, P.; Feng, J. Two-Orbit Switch-Pitch Structures. J. Int. Assoc. Shell Spat. Struct. 2012, 53, 157–162. [Google Scholar]
- Stachel, H. Two Examples of Solids Constructed from Given Developments. J. Geom. Graph. 2016, 20, 225–241. [Google Scholar]
- Mundilova, K. On mathematical folding of curved crease origami: Sliding developables and parametrizations of folds into cylinders and cones. Comput. Des. 2019, 115, 34–41. [Google Scholar] [CrossRef]
- Dias, M.A.; Dudte, L.H.; Mahadevan, L.; Santangelo, C.D. Geometric Mechanics of Curved Crease Origami. Phys. Rev. Lett. 2012, 109, 114301. [Google Scholar] [CrossRef] [PubMed] [Green Version]
- Lee, T.-U.; You, Z.; Gattas, J.M. Elastica surface generation of curved-crease origami. Int. J. Solids Struct. 2018, 136-137, 13–27. [Google Scholar] [CrossRef]
- Gattas, J.; You, Z. The behaviour of curved-crease foldcores under low-velocity impact loads. Int. J. Solids Struct. 2015, 53, 80–91. [Google Scholar] [CrossRef]
- Verma, S.; Epps, G. Curved Folding: Design to Fabrication; Adaptive Architecture: London, UK, 2013. [Google Scholar]
- Chen, Y.; Lu, C.; Yan, J.; Feng, J.; Sareh, P. Intelligent computational design of scalene-faceted flat-foldable tessellations. J. Comput. Des. Eng. 2022, 9, 1765–1774. [Google Scholar] [CrossRef]
- Turrin, M.; von Buelow, P.; Stouffs, R. Design explorations of performance driven geometry in architectural design using parametric modeling and genetic algorithms. Adv. Eng. Inform. 2011, 25, 656–675. [Google Scholar] [CrossRef]
- Hrones, J.; Nelson, G. Analysis of the Four-Bar Linkage: Its Application to the Synthesis of Mechanisms; The MIT Press: London, UK, 1951. [Google Scholar]
- Chung, W.-Y. The characteristics of a coupler curve. Mech. Mach. Theory 2005, 40, 1099–1106. [Google Scholar] [CrossRef]
- Popescu, I.; Sass, L. Mecanisme Generatoare de Curbe; Editura Scrisul Românesc: Craiova, Romania, 2001. [Google Scholar]
- Popescu, I. Noi Mecanisme Generatoare de Curbe; Editura Sitech: Craiova, Romania, 2014. [Google Scholar]
- Popescu, I.; Luca, L.; Cherciu, M.; Marghitu, D. Mechanisms for Generating Mathematical Curves; Springer: Berlin/Heidelberg, Germany, 2020. [Google Scholar] [CrossRef]
- Structuri Spațiale Proiectate Pentru Structuri Complexe Ușoare Procesate prin Curved Crease Folding [CCF–Surf] (Spatial Surfaces Designed for Complex, Light Weight Structures Processed by Curved Crease Folding), Project Manager Raducanu D. Project No. 468PED/23.10.2020–UEFISCDI. Available online: http://www.mdef.pub.ro/research/CCF-Surf/ro/index.html (accessed on 20 September 2022).
- Cojocaru, V.D.; Raducanu, D.; Gloriant, T.; Gordin, D.M.; Cinca, I. Effects of cold-rolling deformation on texture evolution and mechanical properties of Ti-29Nb-9Ta-10Zr alloy. Mater. Sci. Eng. A 2013, 586, 1–10. [Google Scholar] [CrossRef] [Green Version]
- Chahardoli, S.; Nia, A.A. Investigation of mechanical behavior of energy absorbers in expansion and folding modes under axial quasi-static loading in both experimental and numerical methods. Thin-Walled Struct. 2017, 120, 319–332. [Google Scholar] [CrossRef]
Y Length (mm) | Z Length (mm) |
---|---|
91,528.28559563063 | 111.74898641420609 |
91,528.28559563063 | 111.74898641420609 |
91,523.15430668638 | 111.07217245194306 |
91,519.18208890714 | 110.19317830302899 |
91,516.01312827088 | 109.22906114140622 |
… | … |
91,503.4291529919 | 41.979460160407896 |
… | … |
91,502.26663899176 | 27.986920098077377 |
91,501.77185712893 | 19.25441902162445 |
91,501.69319705882 | 17.19924596043298 |
91,501.62696876194 | 14.952772589827951 |
91,501.57967941693 | 12.41294045242803 |
Material | Young’s Modulus (Mpa) | Poisson’s Ratio | Density (kg/mm3) | Yeld Stress (Mpa) | Linear Thermal Expansion Coefficient (K−1) | Thermal Conductivity (W/mm·K) |
---|---|---|---|---|---|---|
Aluminium (6061–T6) | 75.000 × 103 | 0.330 | 2.700 × 10−6 | 241.300 × 100 | 23.500 × 10−6 | 167.000 × 10−3 |
Model No. | Maximum Displacements (mm) | Equivalent Von Mises Stresses (Mpa) |
---|---|---|
1 | 1.097 × 100 | 9.407 × 100 … 1.568 × 103 |
2 | 7.242 × 10−1 | 3.020 × 100 … 1.647 × 103 |
3 | 2.740 × 100 | 3.749 × 101 … 2.958 × 103 |
4 | 2.105 × 10−1 | 6.664 × 100 … 2.792 × 102 |
5 | 1.771 × 100 | 3.807 × 100 … 5.455 × 102 |
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |
© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
Share and Cite
Duta, A.; Popescu, I.; Cretu, S.-M.; Corzanu, A.; Corzanu, V.; Popa, D.-L. The Manufacture of Curved Crease Surfaces Starting from Kinematic Analysis of Planar Mechanisms. Processes 2022, 10, 2344. https://doi.org/10.3390/pr10112344
Duta A, Popescu I, Cretu S-M, Corzanu A, Corzanu V, Popa D-L. The Manufacture of Curved Crease Surfaces Starting from Kinematic Analysis of Planar Mechanisms. Processes. 2022; 10(11):2344. https://doi.org/10.3390/pr10112344
Chicago/Turabian StyleDuta, Alina, Iulian Popescu, Simona-Mariana Cretu, Andrei Corzanu, Valentin Corzanu, and Dragos-Laurentiu Popa. 2022. "The Manufacture of Curved Crease Surfaces Starting from Kinematic Analysis of Planar Mechanisms" Processes 10, no. 11: 2344. https://doi.org/10.3390/pr10112344
APA StyleDuta, A., Popescu, I., Cretu, S. -M., Corzanu, A., Corzanu, V., & Popa, D. -L. (2022). The Manufacture of Curved Crease Surfaces Starting from Kinematic Analysis of Planar Mechanisms. Processes, 10(11), 2344. https://doi.org/10.3390/pr10112344